Download NAME: ALGEBRA 293 8 – 1 Notes: Greatest Common Factor (GCF

NAME: ___________________________________
ALGEBRA 293
8 – 1 Notes: Greatest Common Factor (GCF)
Prime Number: A number that has exactly two factors, itself and 1.
The number 1 is not prime because it only has one factor. The smallest prime number
is 2. Two is also the only even prime number.
Factors: Whole numbers that are multiplied to find a product are called factors of
that product. A number is divisible by its factors.
Product: The result of multiplying two or more factors.
Example: 1 and 8 are factors of 8.
8 is the product of 1 and 8.
8 can also be factored as or as The order of the factors does not change the product.
Prime factorization: When all the factors of a number are written as prime numbers.
Aside from the order of the factors, there is only one way to write the prime factorization
of a number.
Example: Write the prime factorization of 60.
60
2
30
3
10
2
[1]
5
NAME: ___________________________________
ALGEBRA 293
8 – 1 Notes: Greatest Common Factor (GCF)
Example: Write the prime factorization of 98.
98
2
49
7
7
Common factors: Factors that are shared by two or more whole numbers.
Greatest Common Factor, or GCF: The greatest of these common factors
Example: Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 32: 1, 2, 4, 8, 16, 32
Common Factors: 1, 2, 4
Greatest Common Factor: 4
Example: Find the greatest common factor of each pair of numbers.
24 and 60
24
2
60
12
2
2
6
2
30
3
3
10
2
5
The greatest common factor is the product of the prime factors that each has in
common. The greatest common factor of 24 and 60 is [2]